Answer:
[tex]y=100-20x[/tex]
Step-by-step explanation:
Let the x-axis be the time (in years) and the y-axis the value of the fax machine (in dollars).
We know that the initial value of the fax machine is $100; in other words, when the time is zero years, the value is $100, or as an ordered pair (0, 100). We also know that after 1 year the value decreases to $80, so (1, 80).
Now we can find the slope of the line passing through those two points using the slope formula
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
where
[tex]m[/tex] is the slope
[tex](x_1,y_1)[/tex] are the coordinates of the first point
[tex](x_2,y_2)[/tex] are the coordinates of the second point
Replacing values:
[tex]m=\frac{80-100}{1-0}[/tex]
[tex]m=-20[/tex]
Now, to complete our model we are using the point slope formula
[tex]y-y_1=m(x-x_1)[/tex]
where
[tex]m[/tex] is the slope
[tex](x_1,y_1)[/tex] are the coordinates of the first point
Replacing values:
[tex]y-100=-20(x-0)[/tex]
[tex]y-100=-20x[/tex]
[tex]y=-20x+100[/tex]
[tex]y=100-20x[/tex]
We can conclude that the correct linear depreciation model is [tex]y=100-20x[/tex]
